Comparison of Viscoelastic Properties of the Pharyngeal Tissue:Human and Canine

Sung Min Kim, PhD,1 Timothy M. McCulloch, MD,2 and Kwan Rim, PhD31Department of Biomedical Engineering, Yonsei University, College of Medicine, Seoul, Korea;2Department of Otolaryngology, Head & NeckSurgery, College of Medicine, University of Iowa; and3Department of Biomedical Engineering, College of Engineering, University of Iowa,Iowa City, Iowa, USA

Abstract. The viscoelastic properties of the human andcanine pharyngeal tissue in tension were evaluated,based on both an experimental protocol—consisting ofcyclic load, tensile stress relaxation, and incremental stepload tests—and the quasi-linear viscoelastic theory. Thereduced stress relaxation function and the elastic re-sponse of the pharyngeal tissues were derived from theexperimental results specifically obtained from those tis-sues. The characteristic features of viscoelastic propertywere obtained for both human and canine pharyngealtissues by applying the quasi-linear viscoelastic theoryand compared with each other. The material properties ofthe pharyngeal tissue were sought to facilitate the three-dimensional biomechanical model of the pharyngealfunction by using the finite element method.

Key words: Pharyngeal tissue — Quasi-linear — Vis-coelastic properties — Cyclic load test — Tensile stressrelaxation test — Incremental step load test — Biome-chanical model — Finite element method — Deglutition— Deglutition disorders.

The purpose of the present study was to address onemissing prerequisite for a comprehensive biomechanicalanalysis of the viscoelastic properties of the normal pha-ryngeal tissue. This characterization will provide impor-tant information toward understanding the mechanicalproperties of the tissue as a whole. The analytical ap-proach, based on the quasi-linear viscoelastic (QLV)theory of Fung [1] is presented to provide an accuratedescription of the nonlinear time-dependent history of

stress. The rationale behind this approach and the theo-retical description are presented.

The biomechanical investigation of human swal-lowing has a relatively short history in comparison withother well-established fields of biomechanics such as or-thopedic biomechanics and cardiovascular biomechan-ics. A complex orchestration of muscular, respiratory,and connective tissue-related events must occur witheach swallow. Failure of any single component will leadto a breakdown of the entire system, producing a swal-lowing dysfunction. To provide better understanding ofthe complicated mechanism of swallowing, this investi-gation is intended to supply one of the missing parts ofthe whole picture. Therefore, along with other types ofstudies, that is, kinematic investigation with visual im-aging techniques and kinetic investigation by mathemati-cal modeling, viscoelastic material properties of pharyn-geal tissue form a very essential part of biomechanicalmodel of swallowing. Although there have been a num-ber of studies concerning the anatomical similarity of thecanine larynx and the human larynx, few studies havereported on the pharyngeal region. For this reason, it isvery useful to investigate material properties of both spe-cies and compare these characteristics.

The ability to provide adequate treatment for dys-phagia, defined as a swallowing disorder, hinges on theunderstanding of the causes of the disorder. A systematicinvestigation of dysphagia also calls for the developmentof a biomechanical model of swallowing that requires theknowledge of kinematics and kinetics of this physiologi-cal phenomenon in addition to the physical properties ofthe tissues involved at every phase of normal and abnor-mal swallowing. Some progress has been made in thebiomechanical investigation of the oral phase [2,3] andthe esophageal phase [4,5] of swallowing, but the bio-mechanical understanding of the pharyngeal phase ofswallow is still at a formative stage.

Correspondence to:Timothy M. McCulloch, M.D., Department ofOtolaryngology, Head & Neck Surgery, College of Medicine, Univer-sity of Iowa, Iowa City, IA 52242, USA

Dysphagia 14:8–16 (1999)

© Springer-Verlag New York Inc. 1999

For the pharyngeal phase, the previous explor-atory biomechanical investigation may be classified un-der the categories of kinematics [6,7], kinetics [8,9], andelectromyography (EMG) studies [10]. For the histomor-phometric and histopathologic features of the pharyngealtissue, abnormalities in muscle histology have been re-ported frequently for the cricopharyngeus muscle of pa-tients with oculopharyngeal muscular dystrophy, motorneuron disease, and other neurological disorders inwhich dysphagia is a common clinical sign [11,12]. Oneof the primary components in the complex anatomy ofthe pharynx is the fan-shaped posterial pharyngeal tissueconsisting of superior, middle, and inferior constrictormuscle and surrounding connective tissue. The primaryphysiological function of the tissue is involved in pro-pulsion and control of bolus and clearance during thepharyngeal phase.

Methods

Pharyngeal Tissue Dissection

The whole pharyngeal tissue was removed from fresh canine carcassesand human cadavers obtained from the University of Iowa body pro-gram. Three whole human tissues were secured, all adult males be-tween 60 and 70 years, without known history of pharyngeal disordersand with no tissue abnormality. Three tissues from the canine carcasseswith no tissue abnormality were also obtained. The tissue removedfrom each subject consisted of the constrictor muscles and the associ-ated connective tissues, the posterior and lateral pharyngeal mucosa.The superior extent of resection was the superior margin of the superiorconstrictor muscle. The inferior extent was the level of the cricopha-ryngeus muscle. Lateral resection margins were the attachments of thetissues to mandible, tongue base, hyoid bone, and laryngeal cartilage.

The whole pharyngeal tissue, whose anatomical configurationresembled a partial conical shell, assumed the form of relatively flatfan-shaped piece upon removal (Fig. 1). For human tissue, it measuredapproximately 10 cm in length, 8–4 cm in width, and approximately 3mm in thickness. For canine tissue, it is measured approximately 6 cmin length, 6–4 cm in width, and approximately 3.5 mm in thickness.After initial dissection, the tissue was rolled in saline-soaked gauze andstored frozen until the time of testing, which was performed within 48hr of tissue acquisition.

Test Specimen Preparation

For each pharyngeal tissue experiment, five to six tissue specimenswere prepared from one whole defrosted tissue of fresh human cadaverand canine carcass. Each specimen was dissected out of the whole pieceof fan-shaped pharyngeal tissue by carefully cutting parallel to thedirection of the fiber orientation of constrictor muscle (Fig. 1). Mucosaand connective tissue were left intact with the muscle. Dimensions ofeach specimen (thickness, length, and width) were measured with anaccuracy of 0.1 mm by vernier calipers before the tests. The specimenwas loaded between two soft tissue grips, and the gauge length, definedas the distance between the grips, was also measured as the deformationreference because the dimension of the specimen was changing due toloading. In human tissue, the nominal dimensions of each specimen

were 5–6 cm in length, 1–1.5 cm in width, and 0.3–0.33 cm in thick-ness. In canine tissue, the nominal dimensions of each specimen were4–5 cm in length, 0.7–1.2 cm in width, and 0.35–0.42 cm in thickness.The average thickness of the pharyngeal tissue specimens was 0.315 ±0.021 cm in human and 0.412 cm in canine, the mean gauge length ofthe specimens was 4.02 ± 0.706 cm in human and 2.68 cm ± 0.33 cmin canine, and the mean width was 1.279 ± 0.247 cm in human and 1.21± 0.25 cm in canine. The ratio between the initial undeformed statelength (gauge length) and width of the specimen was approximately 4:1in human tissue and 3:1 in canine tissue, which is normally required byAmerican and British standards for uniaxial testing of materials. Aftermeasuring the dimensions of those tissues, specimens were mountedbetween sawtooth-lined brass grips to a length of approximately 10 mmwhile immersed in Ringer’s solution during the tests to preserve theirfreshness as much as possible.

Experimental Apparatus

A small uniaxial hydraulic MTS machine system (Fig. 2) was used toconduct cyclic load, tensile stress relaxation and incremental step loadtests, simple tension test, and one exploratory creep test. A new pro-gram was written to improve the control of the stretch rate and dataacquisition. The Assyst (programming language) was employed forgeneral convenient of data acquisition and reduction.

Experimental Procedures

Because soft tissue in general has a tendency to shrink after removalfrom the subject, it is important to mark the correct undeformed lengthrelative to zero load (zero stress) to ensure the correct measurement.For all the tests, the specimen was stretched to the minimum load andthen unloaded until zero force was again recorded before each test.Dimensions of every specimen were remeasured immediately beforeeach test to ensure the accuracy of the cross-sectional area calculationfor stress (MPa) in SI units. All specimens were tested while immersedin Ringer’s solution at a simulated body temperature of 37°C; thistemperature was maintained in the two-layer glass water jacket by

Fig. 1. Schematic diagram of the whole pharyngeal tissue (posteriorpharyngeal wall). The tissue is composed of constrictor muscle, con-nective tissue, and mucosa. The test specimen for each test was ob-tained from dissecting the tissue horizontally.

S.M. Kim et al.: Human vs. Canine Pharyngeal Tissue 9

circulating water of 37°C that was controlled by a temperature con-troller and monitored by a thermometer during entire procedure. Toprevent the slip between the test specimen and its grips during the test,specially designed soft tissue grips, which were lined with sawteeth inthe contact area, were used to apply firm gripping force against testspecimens. Such a slip, if unchecked, could induce a large experimentalerror in soft tissue measurement. All specimens were securely mountedbetween two grips with special care to avoid damage and slip.

With a set of test specimens prepared from the whole pharyn-geal tissue of each subject, a total of 18 specimens (six specimens wereprepared from one of three subject’s tissue) were tested for differenttests. The tests included a cyclic load test, a tensile stress relaxationtest, an incremental step load test, and a simple tension test. An extraspecimen as a spare and the other specimen for one exploratory test (acreep test) were prepared. Consequently, a total of three sets of tests ofpharyngeal tissue specimens were carried out for the one test protocolunder this experiment. The data originally recorded are expressed asvoltage and elongation in millimeters. All load-elongation curves weredigitized and converted to stress-strain data. To find the stress historyof relaxation function, normalized stress, defined as reduced stressrelaxation, was required from the stress relaxation test. The measuredstress values from stress relaxation test were converted into normalizedstress, expressed ass(t)/s0, wheres(t) is the stress at timet, ands isstress at the beginning of relaxation, i.e., the ratio of the stress at time(t) divided by the stress at the beginning of relaxation.

Experimental Analyses and Results

Following the tradition well-established in the study oflarge deformation, extension ratio (l) and stress (s) wereused to represent the deformation and the stress, respec-tively. They are defined as follows:

l = deformed specimen length~L!/ initial undeformedspecimen length~L!, and

s = internal force~F!/ initial undeformedcross−sectional area~A!.

First, a cyclic load test was conducted with thepharyngeal tissue specimen from each subject, betweenextension ratios ofl 4 1.15 andl 4 1.25. The selectedextension ratios represent 15% and 25% strain, which areassumed to be physiologically functioning deformationlevels. Three such tests were performed at differenttimes, each one of which corresponded to the testing ofthe pharyngeal tissue specimen from one of the threesubjects. A result of this test for 18 cycles of loading andunloading is presented for both human and canine pha-ryngeal tissues in Figure 3, which shows signs of pre-conditioning in the first few cycles and gradual stressrelaxation at both high and low levels of extension.

Second, a tensile stress relaxation test was carriedout with extension ratio atl 4 1.25. A result of this testis presented in Figure 4, which shows that at the exten-sion ratio (l 4 1.25) the stress value decreased about60% from the initial value within first 15 min in bothhuman and canine tissues. It also shows continuous re-laxation process with gradual decrease. It is assumed thatrelaxation of the material shows the sign of maintaininga small variance after a big change in the stress level.

Third, to confirm the relaxation pattern of thetissue, an incremental step load test was performed withthe pharyngeal tissue specimen from each subject, inwhich the specimen was subjected to five incrementalsteps of stretch up tol 4 1.35 at 10-min intervals froml 4 1.1, with the extension ratio interval ofl 4 0.05.The time interval for the test was determined appropri-ately, based on the results of the stress relaxation test andeach level of extension ratiol. The corresponding time-varying stresss(t) at each different extension ratio wasevaluated, and a result of this test is shown in Figure 5.The result shows that same type of stress relaxation be-havior is repeated within the given time intervals.

Because it is required for subsequent QLV char-acterization of the pharyngeal tissue, uniaxial tensiletests were also conducted with the remaining specimensto estimate the elastic response of the tissue. A result ofthe test, in which the specimen was strained at a rate of0.5% per second (dl/dt 4 0.005/sec), is presented inFigure 6. The strain rate is fixed at this level for all

Fig. 2. Experimental apparatus.A The experimental set-up consists ofan MTS machine, a load cell, a double-layer water jacket, a computer,and a water pump. The MTS machine was used for the tensile type oftest including the cyclic load test, stress relaxation, uniaxial tensile test,and incremental load test.B The experimental set-up consists of a loadcell, a double-layer water jacket, and a water pump. The MTS machinewas used for the tensile type of test including the cyclic load test, stressrelaxation, uniaxial tensile test, and incremental load test.

10 S.M. Kim et al.: Human vs. Canine Pharyngeal Tissue

tensile tests during the experiment to ensure reliable re-sults with firm grip throughout preliminary trials.

Quasi-Linear Viscoelastic Characterization

For analytical characterization of the viscoelastic prop-erties of the pharyngeal tissue, the reduced stress relax-ation function and the elastic response were determinedfrom the experimental test results (stress relaxation testand uniaxial tensile test), with the application of the QLVmodel introduced by Fung [1]. In this theory, the time-

history of stress,s[«(t),t], is dependent on both reducedstress relaxation function and elastic response and is ex-pressed as:

s 4 s[«(t),t] ≅ G(t) * Se[«(t)] (1)

where« and t are strain and time, respectively,Se is the‘‘elastic response,’’ andG(t) is the ‘‘reduced stress re-laxation function’’ normalized from stress relaxationfunction, with G(0) 4 1. Because the reduced stressrelaxation functionG(t) is obtained by normalizing thestress relaxation function from the first data point, whichis timet 4 0, G(0) represents first data point.Se andG(t)are obtained from uniaxial tensile test and stress relax-

Fig. 3. Cyclic load test result. During the test the specimen was loadedunder the cyclic loading condition with a 1-sec period. The test wasperformed during 18 cycles (18 sec) and the result shows stress relax-ation after half of the cycles. Human tissue shows more high levelstress relaxation in stress value.

Fig. 4. Stress relaxation test result. The test was performed under theextension ratiol 4 1.25 (L/L0) during a 1-hr period with 3660 datapoints (1 point/1 sec). The result (one averaged human vs. two caninetissues) shows continuous relaxation, but stress values were reducedmore than 60% within first 15 min for both types of tissue. Humantissue shows more high level stress relaxation in stress, which is similarto the cyclic load test result.

Fig. 5. Incremental step load test result. The test was performed toensure the stress relaxation in various extension ratios, with incrementsof l 4 0.05 during a 10-min period. The result shows stress relaxationsimilar to the stress relaxation test result. As expected from the stressrelaxation test result, human tissue shows more high level stress relax-ation in stress value.

Fig. 6. Uniaxial tensile load test result. The test result represents stressversus strain curve. The human tissue shows a more typical nonlineartype of stress-strain curve. The strain rate is maintained with a constantvalue and is controlled by computer during entire test.

S.M. Kim et al.: Human vs. Canine Pharyngeal Tissue 11

ation test results, which are mechanical property func-tions from given materials.

Now, the elastic responseSe is represented by anexponential function of strain,

Se 4 A(eB« − 1) (2)

whereA andB are constants, the coefficients of the elas-tic response, that can be determined from the experimen-tally obtained stress-strain relationship. The values ofAandB estimated by best curve fit are obtained from thecurve fitting function in Crickett software used on alogarithmic transformation of equation (2) for the humanpharyngeal tissue from Figure 6:

A = 3.855 1.75~MPa!B = 0.0565 0.031

For canine tissue,

A = 1.599~MPa!B = 0.192

Because the strain rate, defined asa 4 dl/dt, was keptuniform throughout the simple tension test, i.e.,a 40.5%/sec (dl/dt 4 0.005/sec), the strain,«, can be ex-pressed as a function of time.

« 4 «(t) (3)

Consistent with the Fung’s QLV theory, the stress equa-tion (1) is written more specifically as

s~t! = *−`

tG~t − t! Se@«~t!#dt

= *0

tG~t − t!

dSe ~«!

d«

d«

dtdt, (4)

and the reduced stress relaxation function in equation (1)is approximated in the following form:

G~t! = @1 + C$E1~t/t2! − E1~t/t1!%#/@1 + C ln~t2/t1!#(5a)

where

E1~t! = *0

`

~e−t/t!dt ≈ − g − lnt − (n=1

`

@~−1!n tn/n • n!#,

where g is Euler’s constant, is an exponential integralfunction andC, t1, andt2 are constants determined fromthe experimental data. The set of experimentally ob-tained stress relaxation data were converted into a set ofreduced stress relaxation data {G(t) 4 [s(t)/s(0)]}, i.e.,

the experimental stress relaxation values ofs(t) dividedby the stress data by the stress values(t), at t 4 0.Because, from equation (5),

G~t! =@1 + C$E1~t/t2! − E1~t/t1!%#

@1 + C ln ~t2/t1!#

=

1 + C ln ~t2/t1! + CS(n=1

`~−1!n ~t/t1!n

nn!− (

n=1

`~−1!n ~t/t2!n

nn! D@1 + C ln ~t2/t1!#

(5b)

Therefore, the reduced stress value att 4 0 is 1, whichmeansG(t 4 0) 4 1.

The values ofC, t1 (short time constant), andt2(long time constant) for the pharyngeal tissue were esti-mated by using experimental test results fordG(t)/d ln(t),G(`), andG(t). With approximation of equation (5), i.e.,if t1 andt2 differ sufficiently thatt1 << t << t2 (normallyshort time relaxationt1 is much smaller than long timerelaxation t2) for large values oft, E1(t/t2) is muchgreater thanE1(t/t1); then,

G(t) ≅1 − Cg − C ln~t/t2!

1 + C ln~t2/t1!,

dG~t!

d~lnt!=

−C

1 + C ln~t2/t1!= constant

(6a)

whereg 4 0.577216 is Euler’s constant.Because ast approaches , both E1(t/t1) and

E1(t/t1) go to 0.

G~`! =1

1 + C ln~t2/t1!ast → ` from equation~5!

G(t) behaves as a logarithmic function of time with aconstant slopeb given by equation (6a)

b =dG~t!

d lnt= − CG` (6b)

The slope can be obtained from experimentalstress relaxation test data by using the curve fittingmethod of the reduced stress relaxation curve [13]. ThenparameterC can be obtained.

C 4 −b/G`, (6c)

If we consider the reduced stress relaxation functionG(t)of equation (6a) att 4 1 sec, then we can obtain timeconstants by using equations (6b) and (6c),

t1 = exp@g + ~1 − G1! /b#, (6,d)t2 = exp@g − G1/b − 1/C#, (6,e)

12 S.M. Kim et al.: Human vs. Canine Pharyngeal Tissue

whereG1 is the value ofG(t) at t 4 1 sec, andg 40.577216 is Euler’s constant.

From equations (6), the constants such asG1, G`,and b can be determined with experimental data fromstress relaxation. Therefore, the average values ofC, t1,and t2 are obtained by using those values in equations(6c) through (6e). Those values are as follows:

Humant1 = 0.01145s, C = 0.571, andt2

= 0.62× 105 secCanine

t1 = 0.1747s, C = 1.166, andt2

= 0.11× 105 sec

The stress relaxations of two different species,i.e., human and canine, are rapid initially and becamegradual over time as shown with stress relaxation in Fig-ure 4 and with reduced stress relaxation in Figure 7.After the initial stress relaxation (large decrement of thestress value), overall stress relaxation process of the hu-man and canine pharyngeal tissues apparently wouldhave continued for a more extended period. The mea-surement of long-term relaxation behavior, however, wasdifficult, because of deterioration or environmentally in-duced changes that could affect the results if the experi-ment was prolonged. More than 60% of the initial stressvalue in human pharyngeal tissue was reduced over thefirst 10-min period. For canine tissue, the stress relax-ation process was more rapid than that of human: morethan 70% of the initial stress value was reduced.

Equations (5) through (6) with approximation en-ables one to predict a good estimate of the stress relax-ation behavior in long-term linear portion of the stressrelaxation. Figure 7 shows consistent behaviors betweenthe three specimens in reduced stress relaxation. As de-scribed earlier, these parameters and coefficientsA andBfrom the elastic response in equation (2) are used topredict cyclic test results.

Substitution of equation (2) into equation (4)leads to:

s~t! = AB a *0

tG~t − t!eaBt dt (7)

which, by lettingu = t − t, anddu = − dt, and equation(7) becomes

s~t! = AB aeaBt *0

tG~u!e−aBu du (8)

By using equation (8) and estimated material constantsAandB from elastic response equation (2), theoretical es-

timates of the peak and valley stresses are obtained forthe several cycles of a cyclic load test by numericalintegration and are plotted in Figure 8 in juxtapositionwith the averaged experimental stress values. Except forsome overshoot, which is assumed to be the precondi-tioning process in the experimental stress for the firstcycle peak stress, the theoretical estimates describe rela-tively well the experimentally measured values. Theseresults demonstrated the feasibility of QLV theory todescribe the viscoelastic properties of pharyngeal tissue.As a result, the model may provide the accurate descrip-tion of the mechanical properties of the tissue.

Fig. 8. Cyclic load test (experimental and analytical values). Usingequations and estimated material constants from experimental tests,theoretical estimates of the peak and valley stresses were obtained forseveral cycles of a cyclic load test by numerical integration and areplotted in juxtaposition with the averaged experimental stress values.Except for some overshoot, which was assumed to be the precondi-tioning process for the first cycle peak stress, the theoretical estimatesdescribe the experimentally measured values relatively well.

Fig. 7. Reduced stress relaxation (experimental values). The measuredstress values from the stress relaxation test were converted into nor-malized stress expressed ass(t)/s0, wheres(t) is stress at timet, ands is stress at the beginning of relaxation, i.e., the ratio of the stress attime (t) divided by the stress at the beginning of relaxation.

S.M. Kim et al.: Human vs. Canine Pharyngeal Tissue 13

Discussion

The viscoelastic properties of the human and canine pha-ryngeal tissues are not available in the literature. There-fore, only the characteristic features of the experimen-tally determined viscoelastic property data of the tissuemay be compared with each other and with those of othersoft tissues reported in the literature [13–19].

In the stress relaxation, the overall logarithmicdecay appeared to be nonlinear over relaxation periods of3660 sec. Initial stress was relaxed to below 60% forhuman and 70% for canine tissue over this period andshowed no asymptotic limit. Several investigations [20]have reported similar nonlinear decay of stress relaxationon the logarithmic time scale. However, in the approxi-mation of the reduced stress relaxation curve, a linearapproximation of that function may be possible withinlimited timet. Such a comparison indicates a good quali-tative agreement in every category of cyclic load, tensilestress relaxation, and incremental step load tests. Forexample, the stress relaxation response of the pharyngealtissue is found to be relatively rapid, i.e., the pharyngealtissue behaves like a material with a fading memory.This finding is consistent with the relaxation character-istics of other soft tissues previously reported by Woo etal. [21–25] and Alipour-Haghighi et al. [26–28].

The comparison of canine and human pharyngealtissues showed that all the stress values of human tissuewas higher than those of canine tissue in every testsshow. Those differences may have originated from thedifferent microstructure of those tissues, which camefrom histologically different species. Another possibleanswer for this difference is that humans have a digestingmechanism that is totally different from that of canine. Ingeneral, dogs swallow food directly from the mouth tothe esophagus, with minimal activity of pharyngealmuscle. However, human swallowing normally requiresmore activity in the pharyngeal region. Therefore, thereare more tension forces in human pharyngeal tissue thanin canine pharyngeal tissue. Another interesting point isthat results are totally opposite in the esophageal region.Our preliminary test results confirmed this point and weexpect it to be confirmed with more test results.

The issues of variability in tissue behavior fromone human or canine pharynx to another and variabilityfrom one region of a given pharynx to another (e.g.,inferior vs. superior) should be discussed in further in-vestigations. There may be some variations based on ourexperimental experience. Although three graphs havebeen plotted in Figure 3 (one human and two canines),two of three human results almost overlapped and onehad some deviation. The three human results were aver-aged and plotted with the two results.

Three whole human pharyngeal tissues and threewhole canine pharyngeal tissues were obtained for theexperiment. For a complete process of the experiment,five specimens were used for cyclic, tensile, incrementalstep, stress relaxation, and extra tests of the whole pha-ryngeal tissue. The specimens used in each test camefrom a similar location or region of the whole pharyngealtissue sample to control the size and location of thespecimen for the consistency of the test. In addition, theorientation of the specimen was the same as the horizon-tal direction (Fig. 1) to emphasize the physiological mo-bility of the pharyngeal structure and the movement ofthe pharynx (expansion and contraction while swallow-ing) and because the deformation ratio or the modulus ofelasticity may be different in the vertical direction of thetissue. However, major deformation may include thehorizontal direction of the tissue shown in Figure 1. Be-cause each tissue had a different size and thickness ac-cording to the histological and morphological back-ground of the subject, it was almost impossible to locateexactly the same place in each tissue across samples.

The variability of the tissue location and exten-sion rate may have affected the result, but the effectshould be minor within the same tissue sample. Thus,results were averaged. For example, the average valuesfor the tests of human tissue specimens (Fig. 3) wereused because the results from two of three specimensalmost overlapped and one had some deviations; thus theaveraged human data were plotted with canine data. The± values of the dimensions of the specimen show the sizevariability, but all the stress values were determined fromthe calculation of the cross-sectional area of the speci-men, which normalized size variability. Furthermore, thematerial constantsC, t1, andt2 demonstrated relativelyhigh variation because they were very sensitive to thevalue of the material coefficients obtained from the curvefitting procedure from the reduced stress relaxation ex-periments.

Previous investigations have reported on the ana-tomical, morphological, biochemical, and biomechanicalchanges that ligaments undergo with growth, but therehave been no reports on the effect of age or sex on tensilestrength. Some researchers have pointed out that the dif-ficulty lies not with the manner of evaluation but with theextraordinary sensitivity of the exponents and amplitudesto very small changes of the data. Realizing these diffi-culties, we concluded that, for a living tissue, a viscoelas-ticity law based on the fully relaxed elastic responseswas very difficult to define. In fact, a formulation basedon G(`) may run into difficulty because often it seemsthat one should look into other tests such as creep, hys-teresis, and oscillation to determine the relaxation func-tion. However, this was not the scope of this investiga-tion.

14 S.M. Kim et al.: Human vs. Canine Pharyngeal Tissue

The analytical characterization of the mechanicalproperties of the pharyngeal tissue based on the QLVtheory [1] appears to be feasible. The constitutive equa-tion (7) represents the relaxation and cyclic behavior ofthe pharyngeal tissue fairly well. It is also consistent withwhat has been reported by those who have investigatedother soft tissues [13,16,21–28].

In summary, we have applied the QLV theory toassess the viscoelastic properties of human and caninepharyngeal tissue. The viscoelastic behavior can be de-scribed mathematically by a theoretical relationship forsoft tissue as proposed by Fung [1], and this relationshipassumes that the stress response for an applied strainhistory can be expressed as an integral sum of responsesto arteries of infinitesimal increases in strain in terms ofa reduced relaxation functionG(t) and the elastic re-sponse of the tissue. These expressions contain the ma-terial constantsC, t1, t2, A, andB, which describe theviscoelastic properties of the tissue. They can be deter-mined from experimental data by using a nonlinear least-squares curve fitting procedure. The constants were de-termined from the results of an experimental stress re-laxation test. The QLV theory agreed well with theexperimental data. The experiments forG(t) and the elas-tic response were validated by a second experiment inwhich these equations were used to predict the behaviorof the tissue under cyclic loading. The predicted peakand valley stresses matched well with experimental data.Thus, the QLV theory provides an accurate mathematicaldescription of the time and history-dependent viscoelas-tic properties within the range of strains considered.

The material constantsA andB from the elasticresponse function were determined by estimating thestress-strain relation as an exponential type. The linearregression curve fitting was used to estimate the stress-strain curve with a given exponential type of function.There may be other estimations for this relationship, butwe used the exponential function because it is a morereliable estimation of the curve and is easy to handle inthe expression. The feasibility of this approach was con-firmed by the cyclic experimental data, and the resultsdemonstrate that this approach can be used to assess thenonlinear viscoelastic properties of the pharyngeal tissue.

Conclusions

The viscoelastic properties of the human and canine pha-ryngeal tissue in tension were evaluated, based on bothan experimental protocol—consisting of cyclic load, ten-sile stress relaxation, incremental step load, and simpletension tests—and the QLV theory [1]. This materialcharacterization is an indispensable component of thebiomechanical analysis of the pharyngeal phase of swal-

lowing, the other two components being kinematics andkinetics. This study forms part of work toward the bio-mechanical modeling of the pharyngeal phase of swal-lowing for use in systematic investigations of dysphagia.

In future studies of the material properties of thehuman and canine pharyngeal tissue, it is recommendedthat the effects of age, sex, disease, and other abnormali-ties on tissue also be investigated. For more accuratedescriptions of the mechanical properties, histomorpho-metric and histopathological aspects of the tissue shouldbe considered.

Acknowledgments.We thank the following colleagues at the Universityof Iowa: Professor J.B. Park for the use of his biomaterials laboratoryand Mr. John Winterbottom (Biomedical Engineer) in the Departmentof Biomedical Engineering for his valuable assistance in the testing.We also acknowledge Dr. Adrienne Perlman at the University of Illi-nois for having identified the need for initiating a comprehensive bio-mechanical investigation of the pharyngeal dysphagia while she was acolleague of theirs at the University of Iowa. K. Rim acknowledges thesupport services provided by the Center for Advanced Studies of theUniversity of Iowa.

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